The present invention relates generally to circuitry for performing a convolution function, and, more particularly, to convolution circuitry employing digital samples of two input functions taken at discrete time intervals.
Convolution may be expressed as a mathematical relationship combining two time-varying functions. Convolution is used extensively in the signal processing and communications fields, for example in high-speed digital finite-impulse-response filters, and in pulse compression and detection techniques. For two continuous time-varying functions x(t) and c(t), the convolution of the two functions is given by the expression: ##EQU1## where the symbol .tau. represents an independent time variable.
This expression may have little more than an abstract meaning to those outside the communications field, and the physical meaning of convolution can be more readily understood by means of a graphical representation. For example, an explanation along these lines is provided in a book by B. P. Lathi, "Signals, Systems and Communication," published by John Wiley & Sons, Inc., 1965. Basically, if the two input functions are plotted graphically, convolution can be visualized by folding one of the functions about the zero-time axis, and then translating it along the time axis with respect to the corresponding plot of the other function. At each relative position of the two plotted functions, the value of the convolution function is proportional to the sum of the products of corresponding ordinates on the two curves. If one of the curves is of unit height, the graphical representation simplifies further to one of determining areas under the other curve as one curve is translated with respect to the other.
When the time-varying functions to be convolved are represented by samples taken at discrete time intervals, the corresponding expression for the convolution function is: ##EQU2##
Although many convolution circuits have been suggested in the past, no fully digital circuit has been successfully implemented in monolithic form. Design complexity is among the reasons usually given for lack of success in this area. The inherent advantages of integrated circuitry, including higher speed, lower power and potentially lower cost, have still not resulted in the production of any monolithic convolvers prior to this invention. Accordingly, there has been a definite need for monolithic convolver circuit that is well suited to modern integrated-circuit fabrication techniques utilizing very large scale integration (VLSI). The present invention satisfies this need.